Approximating spatial interactions in a model of forest dynamics
Developments in forest dynamics modelling have led to complex individual-tree distance-dependent models. Questions that arise are: how might such complex models be approximated (possibly through aggregation techniques) to obtain distribution-based models; and, when are such approximated models "equivalent" to the complex models from which they are derived. The approximation process usually involves replacing distance-dependent tree interactions by distance-independent interactions. We used a "toy model" that is derived from an individual-based distance-dependent model of a forest in French Guiana to address these methodological questions. This toy model (model I) was defined in two forms; first a short-range tree interaction (1 in): second for a long-range tree interaction (30 in). Mean-field approximations were used to convert model I into an individual-tree distance-independent model (model II) and into a distribution-based model (model III). If the starting model is model I(long-range), models II and III are shown to be equivalent to each other. Model II is also found to be "consistent" with model I(long-range). Hence. for the toy model considered, long-range interactions can be disregarded, and have no influence on forest growth predictions. On the other hand. model I(short-range) is not equivalent with models II or III. Even so, it was found to be possible to obtain, by ad hoc methods, a distribution-based model (model IV) which, by taking into account the spatial structure generated by short-range interactions, is "consistent" with model I(short range).
| Main Authors: | , |
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| Format: | article biblioteca |
| Language: | eng |
| Subjects: | F62 - Physiologie végétale - Croissance et développement, U10 - Informatique, mathématiques et statistiques, forêt tropicale, dynamique des populations, modèle mathématique, compétition biologique, http://aims.fao.org/aos/agrovoc/c_24904, http://aims.fao.org/aos/agrovoc/c_6111, http://aims.fao.org/aos/agrovoc/c_24199, http://aims.fao.org/aos/agrovoc/c_917, |
| Online Access: | http://agritrop.cirad.fr/526260/ http://agritrop.cirad.fr/526260/1/526260.pdf |
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| Summary: | Developments in forest dynamics modelling have led to complex individual-tree distance-dependent models. Questions that arise are: how might such complex models be approximated (possibly through aggregation techniques) to obtain distribution-based models; and, when are such approximated models "equivalent" to the complex models from which they are derived. The approximation process usually involves replacing distance-dependent tree interactions by distance-independent interactions. We used a "toy model" that is derived from an individual-based distance-dependent model of a forest in French Guiana to address these methodological questions. This toy model (model I) was defined in two forms; first a short-range tree interaction (1 in): second for a long-range tree interaction (30 in). Mean-field approximations were used to convert model I into an individual-tree distance-independent model (model II) and into a distribution-based model (model III). If the starting model is model I(long-range), models II and III are shown to be equivalent to each other. Model II is also found to be "consistent" with model I(long-range). Hence. for the toy model considered, long-range interactions can be disregarded, and have no influence on forest growth predictions. On the other hand. model I(short-range) is not equivalent with models II or III. Even so, it was found to be possible to obtain, by ad hoc methods, a distribution-based model (model IV) which, by taking into account the spatial structure generated by short-range interactions, is "consistent" with model I(short range). |
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